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SECOND EDITION
An Introduction to Machine
Learning Interpretability
An Applied Perspective on Fairness,
Accountability, Transparency,
and Explainable AI
Patrick Hall and Navdeep Gill
Beijing
Boston Farnham Sebastopol
Tokyo
An Introduction to Machine Learning Interpretability, Second Edition
by Patrick Hall and Navdeep Gill
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978-1-098-11545-6
[LSI]
Table of Contents
An Introduction to Machine Learning Interpretability. . . . . . . . . . . . . . . . 1
Definitions and Examples
Social and Commercial Motivations for Machine Learning
Interpretability
A Machine Learning Interpretability Taxonomy for Applied
Practitioners
Common Interpretability Techniques
Limitations and Precautions
Testing Interpretability and Fairness
Machine Learning Interpretability in Action
Looking Forward
2
5
13
17
44
51
53
54
iii
An Introduction to Machine
Learning Interpretability
Understanding and trusting models and their results is a hallmark of
good science. Analysts, engineers, physicians, researchers, scientists,
and humans in general have the need to understand and trust mod‐
els and modeling results that affect our work and our lives. For dec‐
ades, choosing a model that was transparent to human practitioners
or consumers often meant choosing straightforward data sources
and simpler model forms such as linear models, single decision
trees, or business rule systems. Although these simpler approaches
were often the correct choice, and still are today, they can fail in
real-world scenarios when the underlying modeled phenomena are
nonlinear, rare or faint, or highly specific to certain individuals.
Today, the trade-off between the accuracy and interpretability of
predictive models has been broken (and maybe it never really exis‐
ted1). The tools now exist to build accurate and sophisticated model‐
ing systems based on heterogeneous data and machine learning
algorithms and to enable human understanding and trust in these
complex systems. In short, you can now have your accuracy and
interpretability cake...and eat it too.
To help practitioners make the most of recent and disruptive break‐
throughs in debugging, explainability, fairness, and interpretability
techniques for machine learning, this report defines key terms,
introduces the human and commercial motivations for the techni‐
1 Cynthia Rudin, “Please Stop Explaining Black Box Models for High-Stakes Decisions,”
arXiv:1811.10154, 2018, https://arxiv.org/pdf/1811.10154.pdf.
1
ques, and discusses predictive modeling and machine learning from
an applied perspective, focusing on the common challenges of busi‐
ness adoption, internal model documentation, governance, valida‐
tion requirements, and external regulatory mandates. We’ll also
discuss an applied taxonomy for debugging, explainability, fairness,
and interpretability techniques and outline the broad set of available
software tools for using these methods. Some general limitations
and testing approaches for the outlined techniques are addressed,
and finally, a set of open source code examples is presented.
Definitions and Examples
To facilitate detailed discussion and to avoid ambiguity, we present
here definitions and examples for the following terms: interpretable,
explanation, explainable machine learning or artificial intelligence,
interpretable or white-box models, model debugging, and fairness.
Interpretable and explanation
In the context of machine learning, we can define interpretable
as “the ability to explain or to present in understandable terms
to a human,” from “Towards a Rigorous Science of Interpretable
Machine Learning” by Doshi-Velez and Kim.2 (In the recent
past, and according to the Doshi-Velez and Kim definition,
interpretable was often used as a broader umbrella term. That is
how we use the term in this report. Today, more leading
researchers use interpretable to refer to directly transparent
modeling mechanisms as discussed below.) For our working
definition of a good explanation we can use “when you can no
longer keep asking why,” from “Explaining Explanations: An
Approach to Evaluating Interpretability of Machine Learning”
by Gilpin et al.3 These two thoughtful characterizations of inter‐
pretable and explanation link explanation to some machine
learning process being interpretable and also provide a feasible,
abstract objective for any machine learning explanation task.
2 Finale Doshi-Velez and Been Kim, “Towards a Rigorous Science of Interpretable
Machine Learning,” arXiv:1702.08608, 2017, https://arxiv.org/pdf/1702.08608.pdf.
3 Leilani H. Gilpin et al., “Explaining Explanations: An Approach to Evaluating Inter‐
pretability of Machine Learning,” arXiv:1806.00069, 2018, https://arxiv.org/pdf/
1806.00069.pdf.
2
| An Introduction to Machine Learning Interpretability
Explainable machine learning
Getting even more specific, explainable machine learning, or
explainable artificial intelligence (XAI), typically refers to post
hoc analysis and techniques used to understand a previously
trained model or its predictions. Examples of common techni‐
ques include:
Reason code generating techniques
In particular, local interpretable model-agnostic explana‐
tions (LIME) and Shapley values.4,5
Local and global visualizations of model predictions
Accumulated local effect (ALE) plots, one- and twodimensional partial dependence plots, individual condi‐
tional expectation (ICE) plots, and decision tree surrogate
models.6,7,8,9
XAI is also associated with a group of DARPA researchers that
seem primarily interested in increasing explainability in sophis‐
ticated pattern recognition models needed for military and
security applications.
Interpretable or white-box models
Over the past few years, more researchers have been designing
new machine learning algorithms that are nonlinear and highly
accurate, but also directly interpretable, and interpretable as a
term has become more associated with these new models.
4 Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin, “‘Why Should I Trust You?’:
Explaining the Predictions of Any Classifier,” in Proceedings of the 22nd ACM SIGKDD
International Conference on Knowledge Discovery and Data Mining, ACM (2016): 1135–
1144. https://oreil.ly/2OQyGXx.
5 Scott M. Lundberg and Su-In Lee, “A Unified Approach to Interpreting Model Predic‐
tions,” in I. Guyon et al., eds., Advances in Neural Information Processing Systems 30
(Red Hook, NY: Curran Associates, Inc., 2017): 4765–4774. https://oreil.ly/2OWsZYf.
6 Daniel W. Apley, “Visualizing the Effects of Predictor Variables in Black Box Supervised
Learning Models,” arXiv:1612.08468, 2016, https://arxiv.org/pdf/1612.08468.pdf.
7 Trevor Hastie, Robert Tibshirani, and Jerome Friedman, The Elements of Statistical
Learning, Second Edition (New York: Springer, 2009). https://oreil.ly/31FBpoe.
8 Alex Goldstein et al., “Peeking Inside the Black Box: Visualizing Statistical Learning
with Plots of Individual Conditional Expectation,” Journal of Computational and Graph‐
ical Statistics 24, no. 1 (2015), https://arxiv.org/pdf/1309.6392.pdf.
9 Osbert Bastani, Carolyn Kim, and Hamsa Bastani, “Interpreting Blackbox Models via
Model Extraction,” arXiv:1705.08504, 2017, https://arxiv.org/pdf/1705.08504.pdf.
Definitions and Examples
|
3
Examples of these newer Bayesian or constrained variants of
traditional black-box machine learning models include explain‐
able neural networks (XNNs),10 explainable boosting machines
(EBMs), monotonically constrained gradient boosting
machines, scalable Bayesian rule lists,11 and super-sparse linear
integer models (SLIMs).12,13 In this report, interpretable or
white-box models will also include traditional linear models,
decision trees, and business rule systems. Because interpretable
is now often associated with a model itself, traditional black-box
machine learning models, such as multilayer perceptron (MLP)
neural networks and gradient boosting machines (GBMs), are
said to be uninterpretable in this report. As explanation is cur‐
rently most associated with post hoc processes, unconstrained,
black-box machine learning models are usually also said to be at
least partially explainable by applying explanation techniques
after model training. Although difficult to quantify, credible
research efforts into scientific measures of model interpretabil‐
ity are also underway.14 The ability to measure degrees implies
interpretability is not a binary, on-off quantity. So, there are
shades of interpretability between the most transparent whitebox model and the most opaque black-box model. Use more
interpretable models for high-stakes applications or applications
that affect humans.
Model debugging
Refers to testing machine learning models to increase trust in
model mechanisms and predictions.15 Examples of model
debugging techniques include variants of sensitivity (i.e., “What
10 Joel Vaughan et al., “Explainable Neural Networks Based on Additive Index Models,”
arXiv:1806.01933, 2018, https://arxiv.org/pdf/1806.01933.pdf.
11 Hongyu Yang, Cynthia Rudin, and Margo Seltzer, “Scalable Bayesian Rule Lists,” in Pro‐
ceedings of the 34th International Conference on Machine Learning (ICML), 2017, https://
arxiv.org/pdf/1602.08610.pdf.
12 Berk Ustun and Cynthia Rudin, “Supersparse Linear Integer Models for Optimized
Medical Scoring Systems,” Machine Learning 102, no. 3 (2016): 349–391, https://oreil.ly/
31CyzjV.
13 Microsoft Interpret GitHub Repository: https://oreil.ly/2z275YJ.
14 Christoph Molnar, Giuseppe Casalicchio, and Bernd Bischl, “Quantifying Interpretabil‐
ity of Arbitrary Machine Learning Models Through Functional Decomposition,” arXiv:
1904.03867, 2019, https://arxiv.org/pdf/1904.03867.pdf.
15 Debugging Machine Learning Models: https://debug-ml-iclr2019.github.io.
4
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An Introduction to Machine Learning Interpretability
if?”) analysis, residual analysis, prediction assertions, and unit
tests to verify the accuracy or security of machine learning
models. Model debugging should also include remediating any
discovered errors or vulnerabilities.
Fairness
Fairness is an extremely complex subject and this report will
focus mostly on the more straightforward concept of disparate
impact (i.e., when a model’s predictions are observed to be dif‐
ferent across demographic groups, beyond some reasonable
threshold, often 20%). Here, fairness techniques refer to dispa‐
rate impact analysis, model selection by minimization of dispa‐
rate impact, remediation techniques such as disparate impact
removal preprocessing, equalized odds postprocessing, or sev‐
eral additional techniques discussed in this report.16,17 The
group Fairness, Accountability, and Transparency in Machine
Learning (FATML) is often associated with fairness techniques
and research for machine learning, computer science, law, vari‐
ous social sciences, and government. Their site hosts useful
resources for practitioners such as full lists of relevant scholar‐
ship and best practices.
Social and Commercial Motivations for
Machine Learning Interpretability
The now-contemplated field of data science amounts to a superset of the
fields of statistics and machine learning, which adds some technology for
“scaling up” to “big data.” This chosen superset is motivated by commer‐
cial rather than intellectual developments. Choosing in this way is likely
to miss out on the really important intellectual event of the next 50
years.
—David Donoho18
16 Michael Feldman et al., “Certifying and Removing Disparate Impact,” in Proceedings of
the 21st ACM SIGKDD International Conference on Knowledge Discovery and Data Min‐
ing, ACM (2015): 259–268. https://arxiv.org/pdf/1412.3756.pdf.
17 Moritz Hardt et al., “Equality of Opportunity in Supervised Learning,” in Advances in
Neural Information Processing Systems (2016): 3315–3323. https://oreil.ly/2KyRdnd.
18 David Donoho, “50 Years of Data Science,” Tukey Centennial Workshop, 2015, http://
bit.ly/2GQOh1J.
Social and Commercial Motivations for Machine Learning Interpretability
|
5
Among many other applications, machine learning is used today to
make life-altering decisions about employment, bail, parole, and
lending. Furthermore, usage of AI and machine learning models is
likely to become more commonplace as larger swaths of the econ‐
omy embrace automation and data-driven decision making. Because
artificial intelligence, and its to-date most viable subdiscipline of
machine learning, has such broad and disruptive applications, let’s
heed the warning from Professor Donoho and focus first on the
intellectual and social motivations for more interpretability in
machine learning.
Intellectual and Social Motivations
Intellectual and social motivations boil down to trust and under‐
standing of an exciting, revolutionary, but also potentially danger‐
ous technology. Trust and understanding are overlapping, but also
different, concepts and goals. Many of the techniques discussed in
this report are helpful for both, but better suited to one or the other.
Trust is mostly related to the accuracy, fairness, and security of
machine learning systems as implemented through model debug‐
ging and disparate impact analysis and remediation techniques.
Understanding is mostly related to the transparency of machine
learning systems, such as directly interpretable models and explana‐
tions for each decision a system generates.
Human trust of machine learning models
As consumers of machine learning, we need to know that any auto‐
mated system generating a decision that effects us is secure and
accurate and exhibits minimal disparate impact. An illustrative
example of problems and solutions for trust in machine learning is
the Gender Shades project and related follow-up work. As part of
the Gender Shades project, an accuracy and disparate impact prob‐
lem was discovered and then debugged in several commercial facial
recognition systems. These facial recognition systems exhibited
highly disparate levels of accuracy across men and women and
across skin tones. Not only were these cutting-edge models wrong in
many cases, they were consistently wrong more often for women
and people with darker skin tones. Once Gender Shades researchers
pointed out these problems, the organizations they targeted took
remediation steps including creating more diverse training datasets
and devising ethical standards for machine learning projects. In
6
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An Introduction to Machine Learning Interpretability
most cases, the result was more accurate models with less disparate
impact, leading to much more trustworthy machine learning sys‐
tems. Unfortunately, at least one well-known facial recognition sys‐
tem disputed the concerns highlighted by Gender Shades, likely
damaging their trustworthiness with machine learning consumers.
Hacking and adversarial attacks on machine learning systems are
another wide-ranging and serious trust problem. In 2017, research‐
ers discovered that slight changes, such as applying stickers, can pre‐
vent machine learning systems from recognizing street signs.19
These physical adversarial attacks, which require almost no software
engineering expertise, can obviously have severe societal conse‐
quences. For a hacker with more technical expertise, many more
types of attacks against machine learning are possible.20 Models and
even training data can be manipulated or stolen through public APIs
or other model endpoints. So, another key to establishing trust in
machine learning is ensuring systems are secure and behaving as
expected in real time. Without interpretable models, debugging,
explanation, and fairness techniques, it can be very difficult to deter‐
mine whether a machine learning system’s training data has been
compromised, whether its outputs have been altered, or whether the
system’s inputs can be changed to create unwanted or unpredictable
decisions. Security is as important for trust as accuracy or fairness,
and the three are inextricably related. All the testing you can do to
prove a model is accurate and fair doesn’t really matter if the data or
model can be altered later without your knowledge.
Human understanding of machine learning models
Consumers of machine learning also need to know exactly how any
automated decision that affects us is made. There are two intellec‐
tual drivers of this need: one, to facilitate human learning from
machine learning, and two, to appeal wrong machine learning deci‐
sions. Exact explanation of machine-learned decisions is one of the
most fundamental applications of machine learning interpretability
technologies. Explanation enables humans to learn how machine
19 Kevin Eykholt et al., “Robust Physical-World Attacks on Deep Learning Visual Classifi‐
cation,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recogni‐
tion (2018): 1625-1634. https://oreil.ly/2yX8W11.
20 Patrick Hall, “Proposals for Model Vulnerability and Security,” O’Reilly.com (Ideas),
March 20, 2019. https://oreil.ly/308qKm0.
Social and Commercial Motivations for Machine Learning Interpretability
|
7
learning systems make decisions, which can satisfy basic curiosity or
lead to new types of data-driven insights. Perhaps more importantly,
explanation provides a basis for the appeal of automated decisions
made by machine learning models. Consider being negatively
impacted by an erroneous black-box model decision, say for
instance being wrongly denied a loan or parole. How would you
argue your case for appeal without knowing how model decisions
were made? According to the New York Times, a man named Glenn
Rodríguez found himself in this unfortunate position in a penitenti‐
ary in upstate New York in 2016.21 Without information about
exactly why a proprietary black-box model was mistakenly recom‐
mending he remain in prison, he was unable to build a direct case to
appeal that decision. Like the problems exposed by the Gender
Shades study, the inability to appeal automated decisions is not
some far-off danger on the horizon, it’s a present danger. Fortu‐
nately, the technologies exist today to explain even very complex
model decisions, and once understanding and trust can be assured,
broader possibilities for the use of machine learning come into view.
Guaranteeing the promise of machine learning
One of the greatest hopes for data science and machine learning is
simply increased convenience, automation, and organization in our
day-to-day lives. Even today, we are beginning to see fully automa‐
ted baggage scanners at airports and our phones are constantly rec‐
ommending new music (that we might actually like). As these types
of automation and conveniences grow more common, consumers
will likely want to understand them more deeply and machine learn‐
ing engineers will need more and better tools to debug these evermore present decision-making systems. Machine learning also
promises quick, accurate, and unbiased decision making in lifechanging scenarios. Computers can theoretically use machine learn‐
ing to make objective, data-driven decisions in critical situations like
criminal convictions, medical diagnoses, and college admissions,
but interpretability, among other technological advances, is needed
to guarantee the promises of correctness and objectivity. Without
extremely high levels of trust and understanding in machine learn‐
ing decisions, there is no certainty that a machine learning system is
21 Rebecca Wexler, “When a Computer Program Keeps You in Jail,” New York Times, June
13, 2017, https://oreil.ly/2TyHIr5.
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An Introduction to Machine Learning Interpretability
not simply relearning and reapplying long-held, regrettable, and
erroneous human biases. Nor are there any assurances that human
operators, or hackers, have not forced a machine learning system to
make intentionally prejudicial or harmful decisions.
Commercial Motivations
Companies and organizations use machine learning and predictive
models for a very wide variety of revenue- or value-generating
applications. Just a few examples include facial recognition, lending
decisions, hospital release decisions, parole release decisions, or gen‐
erating customized recommendations for new products or services.
Many principles of applied machine learning are shared across
industries, but the practice of machine learning at banks, insurance
companies, healthcare providers, and in other regulated industries is
often quite different from machine learning as conceptualized in
popular blogs, the news and technology media, and academia. It’s
also somewhat different from the practice of machine learning in
the technologically advanced and less regulated digital, ecommerce,
FinTech, and internet verticals.
In commercial practice, concerns regarding machine learning algo‐
rithms are often overshadowed by talent acquisition, data engineer‐
ing, data security, hardened deployment of machine learning apps
and systems, managing and monitoring an ever-increasing number
of predictive models, modeling process documentation, and regula‐
tory compliance.22 Successful entities in both traditional enterprise
and in modern digital, ecommerce, FinTech, and internet verticals
have learned to balance these competing business interests. Many
digital, ecommerce, FinTech, and internet companies, operating out‐
side of most regulatory oversight, and often with direct access to
web-scale, and sometimes unethically sourced, data stores, have
often made web data and machine learning products central to their
business. Larger, more established companies tend to practice statis‐
tics, analytics, and data mining at the margins of their business to
optimize revenue or allocation of other valuable assets. For all these
reasons, commercial motivations for interpretability vary across
industry verticals, but center around improved margins for previ‐
22 Patrick Hall, Wen Phan, and Katie Whitson, The Evolution of Analytics (Sebastopol, CA:
O’Reilly Media, 2016). https://oreil.ly/2Z3eBxk.
Social and Commercial Motivations for Machine Learning Interpretability
|
9
ously existing analytics projects, business partner and customer
adoption of new machine learning products or services, regulatory
compliance, and lessened model and reputational risk.
Enhancing established analytical processes
For traditional and often more-regulated commercial applications,
machine learning can enhance established analytical practices, typi‐
cally by increasing prediction accuracy over conventional but highly
interpretable linear models. Machine learning can also enable the
incorporation of unstructured data into analytical pursuits, again
leading to more accurate model outcomes in many cases. Because
linear models have long been the preferred tools for predictive mod‐
eling, many practitioners and decision-makers are simply suspicious
of machine learning. If nonlinear models—generated by training
machine learning algorithms—make more accurate predictions on
previously unseen data, this typically translates into improved finan‐
cial margins...but only if the model is accepted by internal validation
teams, business partners, and customers. Interpretable machine
learning models and debugging, explanation, and fairness techni‐
ques can increase understanding and trust in newer or more robust
machine learning approaches, allowing more sophisticated and
potentially more accurate models to be used in place of previously
existing linear models.
Regulatory compliance
Interpretable, fair, and transparent models are simply a legal man‐
date in certain parts of the banking, insurance, and healthcare
industries.23 Because of increased regulatory scrutiny, these more
traditional companies typically must use techniques, algorithms,
and models that are simple and transparent enough to allow for
detailed documentation of internal system mechanisms and indepth analysis by government regulators. Some major regulatory
statutes currently governing these industries include the Civil Rights
Acts of 1964 and 1991, the Americans with Disabilities Act, the
Genetic Information Nondiscrimination Act, the Health Insurance
Portability and Accountability Act, the Equal Credit Opportunity
Act (ECOA), the Fair Credit Reporting Act (FCRA), the Fair Hous‐
ing Act, Federal Reserve SR 11-7, and European Union (EU) Greater
23 Fast Forward Labs—Interpretability. https://oreil.ly/301LuM4.
10
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An Introduction to Machine Learning Interpretability
Data Privacy Regulation (GDPR) Article 22.24 These regulatory
regimes, key drivers of what constitutes interpretability in applied
machine learning, change over time or with political winds.
Tools like those discussed in this report are already used to docu‐
ment, understand, and validate different types of models in the
financial services industry (and probably others). Many organiza‐
tions are now also experimenting with machine learning and the
reason codes or adverse actions notices that are mandated under
ECOA and FCRA for credit lending, employment, and insurance
decisions in the United States. If newer machine learning
approaches are used for such decisions, those decisions must be
explained in terms of adverse action notices. Equifax’s NeuroDeci‐
sion is a great example of constraining a machine learning technique
(an MLP) to be interpretable, using it to make measurably more
accurate predictions than a linear model, and doing so in a regulated
space. To make automated credit-lending decisions, NeuroDecision
uses modified MLPs, which are somewhat more accurate than con‐
ventional regression models and also produce the regulatormandated adverse action notices that explain the logic behind a
credit-lending decision. NeuroDecision’s increased accuracy could
lead to credit lending in a broader portion of the market than previ‐
ously possible, such as new-to-credit consumers, increasing the
margins associated with the preexisting linear model techniques.25,26
Shapley values, and similar local variable importance approaches we
will discuss later, also provide a convenient methodology to rank the
contribution of input variables to machine learning model decisions
and potentially generate customer-specific adverse action notices.
Adoption and acceptance
For digital, ecommerce, FinTech, and internet companies today,
interpretability is often an important but secondary concern. Lesstraditional and typically less-regulated companies currently face a
greatly reduced burden when it comes to creating transparent and
24 Andrew Burt, “How Will the GDPR Impact Machine Learning?” O’Reilly.com (Ideas),
May 16, 2018, https://oreil.ly/304nxDI.
25 Hall et al., The Evolution of Analytics.
26 Bob Crutchfield, “Approve More Business Customers,” Equifax Insights Blog, March
16, 2017, https://oreil.ly/2NcWnar.
Social and Commercial Motivations for Machine Learning Interpretability
|
11
trustworthy machine learning products or services. Even though
transparency into complex data and machine learning products
might be necessary for internal debugging, validation, or business
adoption purposes, many newer firms are not compelled by regula‐
tion to prove their models are accurate, transparent, or nondiscrimi‐
natory. However, as the apps and systems that such companies
create (often based on machine learning) continue to change from
occasional conveniences or novelties into day-to-day necessities,
consumer and government demand for accuracy, fairness, and
transparency in these products will likely increase.
Reducing risk
No matter what space you are operating in as a business, hacking of
prediction APIs or other model endpoints and discriminatory
model decisions can be costly, both to your reputation and to your
bottom line. Interpretable models, model debugging, explanation,
and fairness tools can mitigate both of these risks. While direct
hacks of machine learning models still appear rare, there are numer‐
ous documented hacking methods in the machine learning security
literature, and several simpler insider attacks that can change your
model outcomes to benefit a malicious actor or deny service to legit‐
imate customers.27,28,29 You can use explanation and debugging tools
in white-hat hacking exercises to assess your vulnerability to adver‐
sarial example, membership inference, and model stealing attacks.
You can use fair (e.g., learning fair representations, LFR) or private
(e.g., private aggregation of teaching ensembles, PATE) models as an
active measure to prevent many attacks.30,31 Also, real-time disparate
impact monitoring can alert you to data poisoning attempts to
27 Marco Barreno et al., “The Security of Machine Learning,” Machine Learning 81, no. 2
(2010): 121–148. https://oreil.ly/31JwoLL.
28 Reza Shokri et al., “Membership Inference Attacks Against Machine Learning Models,”
IEEE Symposium on Security and Privacy (SP), 2017, https://oreil.ly/2Z22LHI.
29 Nicholas Papernot, “A Marauder’s Map of Security and Privacy in Machine Learning:
An Overview of Current and Future Research Directions for Making Machine Learn‐
ing Secure and Private,” in Proceedings of the 11th ACM Workshop on Artificial Intelli‐
gence and Security, ACM, 2018, https://arxiv.org/pdf/1811.01134.pdf.
30 Rich Zemel et al., “Learning Fair Representations,” in International Conference on
Machine Learning (2013): 325-333. https://oreil.ly/305wjBE.
31 Nicolas Papernot et al., “Scalable Private Learning with PATE,” arXiv:1802.08908, 2018,
https://arxiv.org/pdf/1802.08908.pdf.
12
| An Introduction to Machine Learning Interpretability
change your model behavior to benefit or harm certain groups of
people. Moreover, basic checks for disparate impact should always
be conducted if your model will affect humans. Even if your com‐
pany can’t be sued for noncompliance under FCRA or ECOA, it can
be called out in the media for deploying a discriminatory machine
learning model or violating customer privacy. As public awareness
of security vulnerabilities and algorithmic discrimination grows,
don’t be surprised if a reputational hit in the media results in cus‐
tomers taking business elsewhere, causing real financial losses.
A Machine Learning Interpretability
Taxonomy for Applied Practitioners
A heuristic, practical, and previously defined taxonomy is presented
in this section.32 This taxonomy will be used to characterize the
interpretability of various popular machine learning and statistics
techniques used in commercial data mining, analytics, data science,
and machine learning applications. This taxonomy describes
approaches in terms of:
•
•
•
•
Their ability to promote understanding and trust
Their complexity
The global or local scope of information they generate
The families of algorithms to which they can be applied
Technical challenges as well as the needs and perspectives of differ‐
ent user communities make characterizing machine learning inter‐
pretability techniques a subjective and complicated task. Many other
authors have grappled with organizing and categorizing a variety of
general concepts related to interpretability and explanations. Some
of these efforts include: “A Survey of Methods for Explaining Black
Box Models” by Riccardo Guidotti et al.,33 “The Mythos of Model
Interpretability” by Zachary Lipton,34 “Interpretable Machine Learn‐
32 Patrick Hall, Wen Phan, and SriSatish Ambati, “Ideas on Interpreting Machine Learn‐
ing,” O’Reilly.com (Ideas), March 15, 2017, https://oreil.ly/2H4aIC8.
33 Riccardo Guidotti et al., “A Survey of Methods for Explaining Black Box Models,” ACM
Computing Surveys (CSUR) 51, no. 5 (2018): 93. https://arxiv.org/pdf/1802.01933.pdf.
34 Zachary C. Lipton, “The Mythos of Model Interpretability,” arXiv:1606.03490, 2016,
https://arxiv.org/pdf/1606.03490.pdf.
A Machine Learning Interpretability Taxonomy for Applied Practitioners
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13
ing” by Christoph Molnar,35 “Interpretable Machine Learning: Defi‐
nitions, Methods, and Applications” by W. James Murdoch et al.,36
and “Challenges for Transparency” by Adrian Weller.37 Interested
readers are encouraged to dive into these more technical, detailed,
and nuanced analyses too!
Understanding and Trust
Some interpretability techniques are more geared toward fostering
understanding, some help engender trust, and some enhance both.
Trust and understanding are different, but not orthogonal, phenom‐
ena. Both are also important goals for any machine learning project.
Understanding through transparency is necessary for human learn‐
ing from machine learning, for appeal of automated decisions, and
for regulatory compliance. The discussed techniques enhance
understanding by either providing transparency and specific
insights into the mechanisms of the algorithms and the functions
they create or by providing detailed information for the answers
they provide. Trust grows from the tangible accuracy, fairness, and
security of machine learning systems. The techniques that follow
enhance trust by enabling users to observe or ensure the fairness,
stability, and dependability of machine learning algorithms, the
functions they create, and the answers they generate.
A Scale for Interpretability
The complexity of a machine learning model is often related to its
interpretability. Generally, the more complex and unconstrained the
model, the more difficult it is to interpret and explain. The number
of weights or rules in a model or its Vapnik–Chervonenkis dimen‐
sion, a more formal measure, are good ways to quantify a model’s
complexity. However, analyzing the functional form of a model is
particularly useful for commercial applications such as credit scor‐
ing. The following list describes the functional forms of models and
discusses their degree of interpretability in various use cases.
35 Christoph Molnar, Interpretable Machine Learning (christophm.github.io: 2019),
https://oreil.ly/2YI5ruC.
36 W. James Murdoch et al., “Interpretable Machine Learning: Definitions, Methods, and
Applications,” arXiv:1901.04592, 2019, https://arxiv.org/pdf/1901.04592.pdf.
37 Adrian Weller, “Challenges for Transparency,” arXiv:1708.01870, 2017, https://
arxiv.org/pdf/1708.01870.pdf.
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An Introduction to Machine Learning Interpretability
High interpretability: linear, monotonic functions
Functions created by traditional regression algorithms are prob‐
ably the most interpretable class of models. We refer to these
models here as “linear and monotonic,” meaning that for a
change in any given input variable (or sometimes combination
or function of an input variable), the output of the response
function changes at a defined rate, in only one direction, and at
a magnitude represented by a readily available coefficient.
Monotonicity also enables intuitive and even automatic reason‐
ing about predictions. For instance, if a credit lender rejects
your credit card application, it can easily tell you why because
its probability-of-default model often assumes your credit score,
your account balances, and the length of your credit history are
monotonically related to your ability to pay your credit card bill.
When these explanations are created automatically, they are
typically called adverse action notices or reason codes. Linear,
monotonic functions play another important role in machine
learning interpretability. Besides being highly interpretable
themselves, linear and monotonic functions are also used in
explanatory techniques, including the popular LIME approach.
Medium interpretability: nonlinear, monotonic functions
Although most machine-learned response functions are nonlin‐
ear, some can be constrained to be monotonic with respect to
any given independent variable. Although there is no single
coefficient that represents the change in the response function
output induced by a change in a single input variable, nonlinear
and monotonic functions do always change in one direction as a
single input variable changes. They usually allow for the genera‐
tion of plots that describe their behavior and both reason codes
and variable importance measures. Nonlinear, monotonic
response functions are therefore fairly interpretable and poten‐
tially suitable for use in regulated applications.
(Of course, there are linear, nonmonotonic machine-learned
response functions that can, for instance, be created by the mul‐
tivariate adaptive regression splines (MARS) approach. These
functions could be of interest for your machine learning project
and they likely share the medium interpretability characteristics
of nonlinear, monotonic functions.)
A Machine Learning Interpretability Taxonomy for Applied Practitioners
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15
Low interpretability: nonlinear, nonmonotonic functions
Most machine learning algorithms create nonlinear, nonmono‐
tonic response functions. This class of functions is the most dif‐
ficult to interpret, as they can change in a positive and negative
direction and at a varying rate for any change in an input vari‐
able. Typically, the only standard interpretability measures these
functions provide are relative variable importance measures.
You should use a combination of several techniques, presented
in the sections that follow, to interpret, explain, debug, and test
these extremely complex models. You should also consider the
accuracy, fairness, and security problems associated with blackbox machine learning before deploying a nonlinear, nonmono‐
tonic model for any application with high stakes or that affects
humans.
Global and Local Interpretability
It’s often important to understand and test your trained model on a
global scale, and also to zoom into local regions of your data or your
predictions and derive local information. Global measures help us
understand the inputs and their entire modeled relationship with
the prediction target, but global interpretations can be highly
approximate in some cases. Local information helps us understand
our model or predictions for a single row of data or a group of simi‐
lar rows. Because small parts of a machine-learned response func‐
tion are more likely to be linear, monotonic, or otherwise wellbehaved, local information can be more accurate than global
information. It’s also very likely that the best analysis of a machine
learning model will come from combining the results of global and
local interpretation techniques. In subsequent sections we will use
the following descriptors to classify the scope of an interpretable
machine learning approach:
Global interpretability
Some machine learning interpretability techniques facilitate
global measurement of machine learning algorithms, their
results, or the machine-learned relationships between the pre‐
diction target(s) and the input variables across entire partitions
of data.
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An Introduction to Machine Learning Interpretability
Local interpretability
Local interpretations promote understanding of small regions
of the machine-learned relationship between the prediction tar‐
get(s) and the input variables, such as clusters of input records
and their corresponding predictions, or deciles of predictions
and their corresponding input rows, or even single rows of data.
Model-Agnostic and Model-Specific Interpretability
Another important way to classify model interpretability techniques
is to determine whether they are model agnostic, meaning they can
be applied to different types of machine learning algorithms, or
model specific, meaning techniques that are applicable only for a sin‐
gle type or class of algorithm. For instance, the LIME technique is
model agnostic and can be used to interpret nearly any set of
machine learning inputs and machine learning predictions. On the
other hand, the technique known as Tree SHAP is model specific
and can be applied only to decision tree models. Although modelagnostic interpretability techniques are convenient, and in some
ways ideal, they often rely on surrogate models or other approxima‐
tions that can degrade the accuracy of the information they provide.
Model-specific interpretation techniques tend to use the model to be
interpreted directly, leading to potentially more accurate measure‐
ments.
Common Interpretability Techniques
Many credible techniques for training interpretable models and
gaining insights into model behavior and mechanisms have existed
for years. Many others have been put forward in a recent flurry of
research. This section of the report discusses many such techniques
in terms of the proposed machine learning interpretability taxon‐
omy. The section begins by discussing data visualization approaches
because having a strong understanding of a dataset is a first step
toward validating, explaining, and trusting models. We then present
white-box modeling techniques, or models with directly interpreta‐
ble inner workings, followed by techniques that can generate
explanations for the most complex types of predictive models such
as model visualizations, reason codes, and global variable impor‐
tance measures. We conclude the section by discussing approaches
for testing and debugging machine learning models for fairness, sta‐
bility, and trustworthiness. The techniques introduced in this sec‐
Common Interpretability Techniques
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17
tion will get you well on your way to using interpretable models and
debugging, explanation, and fairness techniques.
Seeing and Understanding Your Data
Seeing and understanding data is important for interpretable
machine learning because models represent data, and understanding
the contents of that data helps set reasonable expectations for model
behavior and output. Unfortunately, most real datasets are difficult
to see and understand because they have many variables and many
rows. Even though plotting many dimensions is technically possible,
doing so often detracts from, instead of enhances, human under‐
standing of complex datasets. Of course, there are many, many ways
to visualize datasets. We chose the techniques highlighted in Tables
1-1 and 1-2 and in Figure 1-1 because they help illustrate many
important aspects of a dataset in just two dimensions.
Table 1. A description of 2D projection data visualization approaches
Technique: 2D projections
Description: Projecting rows of a dataset from a usually high-dimensional original space into a
more visually understandable lower-dimensional space, ideally two or three dimensions. Some
techniques to achieve this include principal components analysis (PCA), multidimensional scaling
(MDS), t-distributed stochastic neighbor embedding (t-SNE), and autoencoder networks.
Suggested usage: The key idea is to represent the rows of a dataset in a meaningful lowdimensional space. Datasets containing images, text, or even business data with many variables can
be difficult to visualize as a whole. These projection techniques enable high-dimensional datasets to
be projected into representative low-dimensional spaces and visualized using the trusty old scatter
plot technique. A high-quality projection visualized in a scatter plot should exhibit key structural
elements of a dataset, such as clusters, hierarchy, sparsity, and outliers. 2D projections are often
used in fraud or anomaly detection to find outlying entities, like people, transactions, or computers,
or unusual clusters of entities.
References:
Laurens van der Maaten and Geoffrey Hinton, “Visualizing Data Using t-SNE,” Journal of Machine
Learning Research, 9 (2008): 2579-2605. https://oreil.ly/2KIAaOtf.
T. F. Cox, Multidimensional Scaling (London: Chapman and Hall, 2001).
Hastie et al., The Elements of Statistical Learning, Second Edition.
G. E. Hinton and R. R. Salakhutdinov. “Reducing the Dimensionality of Data with Neural Networks.”
Science, 13, July 28, 2006. https://oreil.ly/2yZbCvi.
OSS:
h2o.ai (note the H2O Aggregator sampling routine)
R (various packages)
scikit-learn (various functions)
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An Introduction to Machine Learning Interpretability
Global or local scope: Global and local. Can be used globally to see a coarser view of the entire
dataset, or provide granular views of local portions of the dataset by panning, zooming, and drilldown.
Best-suited complexity: Any. 2D projections
can help us understand very complex
relationships in datasets and models.
Model specific or model agnostic: Model
agnostic; visualizing complex datasets with
many variables.
Trust and understanding: Projections add a degree of trust if they are used to confirm machine
learning modeling results. For instance, if known hierarchies, classes, or clusters exist in training or
test datasets and these structures are visible in 2D projections, it is possible to confirm that a
machine learning model is labeling these structures correctly. A secondary check is to confirm that
similar attributes of structures are projected relatively near one another and different attributes of
structures are projected relatively far from one another. Consider a model used to classify or cluster
marketing segments. It is reasonable to expect a machine learning model to label older, richer
customers differently than younger, less affluent customers, and moreover to expect that these
different groups should be relatively disjoint and compact in a projection, and relatively far from
one another.
Table 2. A description of the correlation network graph data visualization
approach
Technique: Correlation network graphs
Description: A correlation network graph is a 2D representation of the relationships (correlation) in
a dataset. The authors create correlation graphs in which the nodes of the graph are the variables in
a dataset and the edge weights (thickness) between the nodes are defined by the absolute values
of their pairwise Pearson correlation. For visual simplicity, absolute weights below a certain
threshold are not displayed, the node size is determined by a node’s number of connections (node
degree), node color is determined by a graph community calculation, and node position is defined
by a graph force field algorithm. The correlation graph allows us to see groups of correlated
variables, identify irrelevant variables, and discover or verify important, complex relationships that
machine learning models should incorporate, all in two dimensions.
Suggested usage: Correlation network graphs are especially powerful in text mining or topic
modeling to see the relationships between entities and ideas. Traditional network graphs—a
similar approach—are also popular for finding relationships between customers or products in
transactional data and for use in fraud detection to find unusual interactions between entities like
people or computers.
OSS:
Gephi
corr_graph
Global or local scope: Global and local. Can be used globally to see a coarser view of the entire
dataset, or provide granular views of local portions of the dataset by panning, zooming, and drilling
down.
Best-suited complexity: Any, but becomes
difficult to understand with more than several
thousand variables.
Model specific or model agnostic: Model
agnostic; visualizing complex datasets with
many variables.
Common Interpretability Techniques
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19
Trust and understanding: Correlation network graphs promote understanding by displaying
important and complex relationships in a dataset. They can enhance trust in a model if variables
with thick connections to the target are important variables in the model, and we would expect a
model to learn that unconnected variables are not very important. Also, common sense
relationships displayed in the correlation graph should be reflected in a trustworthy model.
Figure 1. A correlation network graph is helpful for enhancing trust
and understanding in machine learning models because it displays
important, complex relationships between variables in a dataset as
edges and nodes in an undirected graph. (Figure courtesy of H2O.ai.)
Techniques for Creating White-Box Models
When starting a machine learning endeavor, it’s a best practice to
determine to what degree your model could impact human beings
or be used for other high-stakes decisions. In these high-stakes
cases, maximum transparency safeguards against fairness and secu‐
rity issues. Also, with newer white-box modeling methods like
XNN, monotonic GBM, and scalable Bayesian rule lists, interpreta‐
bility comes at a minimal accuracy penalty, if any at all. Starting with
an interpretable model will likely make subsequent debugging,
explanation, and fairness auditing tasks easier too. The techniques
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An Introduction to Machine Learning Interpretability
in Tables 1-3 through 1-8 will enable you to create highly transpar‐
ent models, potentially well-suited for regulated industry or other
vital applications in which interpretability is of extreme importance.
Table 3. A description of the decision tree white-box modeling approach
Technique: Decision trees
Description: Decision trees create a model that predicts the value of a target variable based on
several input variables. Decision trees are directed graphs in which each interior node corresponds
to an input variable. There are edges to child nodes for values of the input variable that creates the
highest target purity in each child. Each terminal node or leaf node represents a value of the target
variable given the values of the input variables represented by the path from the root to the leaf.
These paths can be visualized or explained with simple if-then rules. In short, decision trees are
data-derived flowcharts.
Suggested usage: Decision trees are great for training simple, transparent models on IID data—
data where a unique customer, patient, product, or other entity is represented in each row. They
are beneficial when the goal is to understand relationships between the input and target variable
with “Boolean-like” logic. Decision trees can also be displayed graphically in a way that is easy for
nonexperts to interpret.
References:
L. Breiman et al., Classification and Regression Trees (Boca Raton, FL: CRC Press, 1984).
Hastie et al., The Elements of Statistical Learning, Second Edition.
OSS:
rpart
scikit-learn (various functions)
Global or local scope: Global.
Best-suited complexity: Low to medium. Decision trees can be complex nonlinear, nonmonotonic
functions, but their accuracy is sometimes lower than more sophisticated models for complex
problems and large trees can be difficult to interpret.
Model specific or model agnostic: Model specific.
Trust and understanding: Increases trust and understanding because input to target mappings
follows a decision structure that can be easily visualized, interpreted, and compared to domain
knowledge and reasonable expectations.
Common Interpretability Techniques
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21
Table 4. A description of the XNN modeling approach and artificial
neural network (ANN) explanations
Technique: XNN and ANN explanations
Description: XNN, a new type of constrained artificial neural network, and new model-specific
explanation techniques have recently made ANNs much more interpretable and explainable. Many
of the breakthroughs in ANN explanation stem from derivatives of the trained ANN with respect to
input variables. These derivatives disaggregate the trained ANN response function prediction into
input variable contributions. Calculating these derivatives is much easier than it used to be due to
the proliferation of deep learning toolkits such as Tensorflow.
Suggested usage: While most users will be familiar with the widespread use of ANNs in pattern
recognition, they are also used for more traditional data mining applications such as fraud
detection, and even for regulated applications such as credit scoring. Moreover, ANNs can now be
used as accurate and explainable surrogate models, potentially increasing the fidelity of both global
and local surrogate model techniques.
References:
M. Ancona et al., “Towards Better Understanding of Gradient-Based Attribution Methods for Deep
Neural Networks,” ICLR 2018. https://oreil.ly/2H6v1yz.
Joel Vaughan et al. “Explainable Neural Networks Based on Additive Index Models,” arXiv:
1806.01933, 2018. https://arxiv.org/pdf/1806.01933.pdf.
OSS:
DeepLift
Integrated-Gradients
shap
Skater
Global or local scope: XNNs are globally interpretable. Local ANN explanation techniques can be
applied to XNNs or nonconstrained ANNs.
Best-suited complexity: Any. XNNs can be
used to directly model nonlinear, nonmonotonic
phenomena but today they often require manual
variable selection. ANN explanation techniques
can be used for very complex models.
Model specific or model agnostic: As
directly interpretable models, XNNs rely on
model-specific mechanisms. Used as surrogate
models, XNNs are model agnostic. ANN
explanation techniques are generally model
specific.
Trust and understanding: XNN techniques are typically used to make ANN models themselves
more understandable or as surrogate models to make other nonlinear models more
understandable. ANN explanation techniques make ANNs more understandable.
22
| An Introduction to Machine Learning Interpretability
Table 5. A description of the monotonic gradient boosting machine (GBM)
white-box modeling approach
Technique: Monotonic GBMs
Description: Monotonicity constraints can turn difficult-to-interpret nonlinear, nonmonotonic
models into interpretable, nonlinear, monotonic models. One application of this can be achieved
with monotonicity constraints in GBMs by enforcing a uniform splitting strategy in constituent
decision trees, where binary splits of a variable in one direction always increase the average value
of the dependent variable in the resultant child node, and binary splits of the variable in the other
direction always decrease the average value of the dependent variable in the other resultant child
node.
Suggested usage: Potentially appropriate for most traditional data mining and predictive
modeling tasks, even in regulated industries, and potentially for consistent adverse action notice or
reason code generation (which is often considered a gold standard of model explainability).
Reference:
XGBoost Documentation
OSS:
h2o.ai
XGBoost
Interpretable Machine Learning with Python
Global or local scope:
Global.
Best-suited complexity: Medium to high.
Monotonic GBMs create nonlinear, monotonic
response functions.
Model specific or model agnostic: As
implementations of monotonicity constraints
vary for different types of models in practice,
they are a model-specific interpretation
technique.
Trust and understanding: Understanding is
increased by enforcing straightforward
relationships between input variables and the
prediction target. Trust is increased when
monotonic relationships, reason codes, and
detected interactions are parsimonious with
domain expertise or reasonable expectations.
Table 6. A description of alternative regression white-box modeling
approaches
Technique: Logistic, elastic net, and quantile regression and generalized additive models (GAMs)
Description: These techniques use contemporary methods to augment traditional, linear modeling
methods. Linear model interpretation techniques are highly sophisticated and typically model
specific, and the inferential features and capabilities of linear models are rarely found in other
classes of models. These types of models usually produce linear, monotonic response functions with
globally interpretable results like those of traditional linear models but often with a boost in
predictive accuracy.
Suggested usage: Interpretability for regulated industries; these techniques are meant for
practitioners who just can’t use complex machine learning algorithms to build predictive models
because of interpretability concerns or who seek the most interpretable possible modeling results.
Common Interpretability Techniques
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23
References:
Hastie et al., The Elements of Statistical Learning, Second Edition.
R. Koenker, Quantile Regression (Cambridge, UK: Cambridge University Press, 2005).
OSS:
gam
ga2m (explainable boosting machine)
glmnet
h2o.ai
quantreg
scikit-learn (various functions)
Global or local scope: Alternative regression
techniques often produce globally interpretable
linear, monotonic functions that can be
interpreted using coefficient values or other
traditional regression measures and statistics.
Best-suited complexity: Low to medium.
Alternative regression functions are generally
linear, monotonic functions. However, GAM
approaches can create complex nonlinear
response functions.
Model specific or model agnostic: Model specific.
Trust and understanding: Understanding is enabled by the lessened assumption burden, the
ability to select variables without potentially problematic multiple statistical significance tests, the
ability to incorporate important but correlated predictors, the ability to fit nonlinear phenomena,
and the ability to fit different quantiles of the data’s conditional distribution. Basically, these
techniques are trusted linear models but used in new, different, and typically more robust ways.
Table 7. A description of rule-based white-box modeling approaches
Technique: Rule-based models
Description: A rule-based model is a type of model that is composed of many simple Boolean
statements that can be built by using expert knowledge or learning from real data.
Suggested usage: Useful in predictive modeling and fraud and anomaly detection when
interpretability is a priority and simple explanations for relationships between inputs and targets
are desired, but a linear model is not necessary. Often used in transactional data to find simple,
frequently occurring pairs or triplets of items or entities.
Reference:
Pang-Ning Tan, Michael Steinbach, and Vipin Kumar, An Introduction to Data Mining, First Edition
(Minneapolis: University of Minnesota Press, 2006), 327-414.
OSS:
RuleFit
arules
FP-growth
Scalable Bayesian Rule Lists
Skater
Global or local scope: Rule-based
models can be both globally and locally
interpretable.
24
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Best-suited complexity: Low to medium. Most
rule-based models are easy to follow for users
because they obey Boolean logic (“if, then”). Rules
can model extremely complex nonlinear,
nonmonotonic phenomena, but rule lists can become
very long in these cases.
An Introduction to Machine Learning Interpretability
Model specific or model agnostic:
Model specific; can be highly interpretable
if rules are restricted to simple
combinations of input variable values.
Trust and understanding: Rule-based models
increase understanding by creating straightforward,
Boolean rules that can be understood easily by users.
Rule-based models increase trust when the generated
rules match domain knowledge or reasonable
expectations.
Table 8. A description of the SLIM white-box modeling approach
Technique: SLIMs
Description: SLIMs create predictive models that require users to only add, subtract, or multiply
values associated with a handful of input variables to generate accurate predictions.
Suggested usage: SLIMs are perfect for high-stakes situations in which interpretability and
simplicity are critical, similar to diagnosing newborn infant health using the well-known Agpar
scale.
Reference:
Berk Ustun and Cynthia Rudin, “Supersparse Linear Integer Models for Optimized Medical Scoring
Systems,” Machine Learning 102, no. 3 (2016): 349–391. https://oreil.ly/31CyzjV.
Software:
slim-python
Global or local scope:
Global.
Best-suited complexity: Low. SLIMs are simple,
linear models.
Model specific or model agnostic: Model
specific; interpretability for SLIMs is
intrinsically linked to their linear nature and
model-specific optimization routines.
Trust and understanding: SLIMs enhance
understanding by breaking complex scenarios into
simple rules for handling system inputs. They
increase trust when their predictions are accurate
and their rules reflect human domain knowledge or
reasonable expectations.
Techniques for Enhancing Interpretability in Complex
Machine Learning Models
The techniques in this section can be paired with interpretable mod‐
els to create visual explanations, generate reason codes, or, poten‐
tially, create adverse action notices. Many of these techniques can be
used to generate explanations for models of arbitrary complexity.
So...no more black boxes!
Seeing model mechanisms with model visualizations
Model visualization techniques provide graphical insights into the
prediction behavior of nearly any machine learning model and help
debug the prediction mistakes they might make. ALE plots, decision
tree surrogate models, ICE plots, partial dependence plots, and
Common Interpretability Techniques
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25
residual plots are presented in Tables 1-9 to 1-13 and in Figures 1-2
and 1-3. ALE plots make up for some well-known shortcomings of
partial dependence plots, surrogate models are simple models of
more complex models, and decision tree surrogate models
(Figure 1-2) create an approximate overall flowchart of a complex
model’s decision-making processes. ICE plots and partial depend‐
ence plots (Figure 1-3) provide a local and global view, respectively,
into how a model’s predictions change based on certain input vari‐
ables. Residual analysis provides a mechanism to visualize any mod‐
el’s prediction errors while also highlighting anomalous data and
outliers that might have undue influence on a model’s predictions,
and in just two dimensions too.
Interestingly, decision tree surrogates, partial dependence plots, and
ICE plots can be used together to highlight potential interactions in
machine learning models. Figures 1-2 and 1-3 were generated from
the same GBM model of a simulated function with known interac‐
tions between input variables num1 and num4 and between inputs
num8 and num9. Notice how the ICE curves diverge from partial
dependence for the values ~-1 < num9 < ~1 in Figure 1-3. Compare
this to the surrogate decision tree in Figure 1-2 for roughly the same
values of num9 to see how the known interactions are represented.
Table 9. A description of the ALE model visualization technique
Technique: ALE plots
Description: ALE plots show us the overall behavior of a machine-learned response function with
respect to an input variable without having to worry too much about correlations or interactions
that could affect the trustworthiness of partial dependence plots. Like partial dependence plots, ALE
plots show the shape—i.e., nonlinearity, nonmonotonicity—of the relationship between
predictions and input variable values, even for very complex models.
Suggested usage: ALE plots are especially valuable when strong correlations or interactions exist
in the training data, situations where partial dependence is known to fail. ALE plots can also be
used to verify monotonicity of response functions under monotonicity constraints and can be used
to check and confirm partial dependence plots. Note that most implementations are in R.
Reference:
Daniel Apley, “Visualizing the Effects of Predictor Variables in Black Box Supervised Learning
Models,” arXiv:1612.08468, 2016, https://arxiv.org/pdf/1612.08468.pdf.
OSS:
ALEPlot
DALEX
iml
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An Introduction to Machine Learning Interpretability
Global or local scope: ALE plots are global in Best-suited complexity: Any. Can be used to
terms of the rows of a dataset but local in
describe almost any function, including complex
terms of the input variables.
nonlinear, nonmonotonic functions.
Model specific or model agnostic: Model agnostic.
Trust and understanding: ALE plots enhance understanding by showing the nonlinearity or nonmonotonicity of the learned response between an input variable and a dependent variable in
complex models. They can enhance trust when displayed relationships conform to domain
knowledge.
Table 10. A description of the decision tree surrogate model visualization
technique
Technique: Decision tree surrogates
Description: A decision tree surrogate model is a simple model that is used to explain a complex
model. Decision tree surrogate models are usually created by training a decision tree on the original
inputs and predictions of a complex model. Variable importance, trends, and interactions displayed
in the surrogate model are then assumed to be indicative of the internal mechanisms of the
complex model. There are few, possibly no, theoretical guarantees that the simple surrogate model
is highly representative of the more complex model.
Suggested usage: Use decision tree surrogate models to create approximate flowcharts of a more
complex model’s decision-making processes. Variables that are higher or used more frequently in
the surrogate tree should be more important. Variables that are above and below one another can
have strong interactions. Use surrogate trees with ICE and partial dependence to find and confirm
interactions, as shown in Figures 1-2 and 1-3.
References:
Mark W. Craven and Jude W. Shavlik, “Extracting Tree-Structured Representations of Trained
Networks,” Advances in Neural Information Processing Systems (1996): 24-30. http://bit.ly/2FU4DK0.
Bastani et al., “Interpreting Blackbox Models via Model Extraction.”
OSS:
iml
Skater
Interpretable Machine Learning with Python
Global or local scope: Generally global. However, there is nothing to preclude using decision tree
surrogate models in the LIME framework to explain more local regions of a complex model’s
predictions.
Best-suited complexity: Any. Surrogate models can help explain machine learning models of
medium-to-high complexity, including nonlinear, monotonic or nonmonotonic models, but if the
surrogate itself becomes large it can be difficult to interpret.
Model specific or model agnostic: Model agnostic.
Trust and understanding: Decision tree surrogate models enhance trust when their variable
importance, trends, and interactions are aligned with human domain knowledge and reasonable
expectations of modeled phenomena. Decision tree surrogate models enhance understanding
because they provide insight into the internal mechanisms of complex models.
Common Interpretability Techniques
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27
Figure 2. A visualization of a decision tree surrogate model as an
approximate overall flowchart of the decision policies learned by a
more complex machine learning model. In this simulated example,
strong interactions exist between the input variables num1 and num4
and between num8 and num9. The call-out box (top left) emphasizes
that the highlighted branches are part of a larger decision tree surro‐
gate model. The highlighted branches allow for comparison to
Figure 1-3. (Figure courtesy of Patrick Hall and H2O.ai.)
Table 11. A description of the ICE plot model visualization technique
Technique: ICE plots
Description: ICE plots are a newer, local, and less well-known adaptation of partial dependence
plots. They depict how a model behaves for a single row of data (i.e., per observation). ICE pairs
nicely with partial dependence in the same plot to provide local information to augment the global
information provided by partial dependence. When ICE curves diverge from partial dependence
curves as in Figure 1-3, this may indicate strong interactions between input variables.
Suggested usage: ICE plots can be used to create local, per-observation explanations using the
same ideas as partial dependence plots. ICE can be used to verify monotonicity constraints and to
detect when partial dependence fails in the presence of strong interactions or correlation among
input variables.
Reference:
Alex Goldstein et al., “Peeking Inside the Black Box: Visualizing Statistical Learning with Plots of
Individual Conditional Expectation,” Journal of Computational and Graphical Statistics 24, no.
1(2015): 44-65. https://arxiv.org/abs/1309.6392.
OSS:
ICEbox
iml
PyCEbox
Interpretable Machine Learning with Python
28
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An Introduction to Machine Learning Interpretability
Global or local scope: Local.
Best-suited complexity: Any. Can be used to describe nearly any function, including nonlinear,
nonmonotonic functions.
Model specific or model agnostic: Model agnostic.
Trust and understanding: ICE plots enhance understanding by showing the nonlinearity, nonmonotonicity, and two-way interactions between input variables and a target variable in complex
models, per observation. They can also enhance trust when displayed relationships conform to
domain knowledge.
Table 12. A description of the partial dependence plot model visualization
technique
Technique: Partial dependence plots
Description: Partial dependence plots show us the average manner in which machine-learned
response functions change based on the values of one or two input variables of interest, while
averaging out the effects of all other input variables.
Suggested usage: Partial dependence plots show the nonlinearity, nonmonotonicity, and twoway interactions in very complex models and can be used to verify monotonicity of response
functions under monotonicity constraints. They pair nicely with ICE plots, and ICE plots can reveal
inaccuracies in partial dependence due to the presence of strong interactions as in Figure 1-3,
where ICE and partial dependence curves diverge. Also, pairing partial dependence and ICE with a
histogram of the variable of interest gives good insight into whether any plotted prediction is
trustworthy and supported by training data. Use partial dependence with either ICE or use ALE plots
instead of partial dependence alone if you suspect your dataset contains correlated or interacting
variables.
Reference:
Hastie et al., The Elements of Statistical Learning, Second Edition.
OSS:
DALEX
h2o.ai
iml
pdp
PDPBox
scikit-learn (various functions)
Skater
Interpretable Machine Learning with Python
Global or local scope: Partial dependence
Best-suited complexity: Any. Can be used to
plots are global in terms of the rows of a
describe almost any function, including complex
dataset but local in terms of the input variables. nonlinear, nonmonotonic functions.
Model specific or model agnostic: Model agnostic.
Trust and understanding: Partial dependence plots enhance understanding by showing the
nonlinearity, nonmonotonicity, and two-way interactions between input variables and a dependent
variable in complex models. They can also enhance trust when displayed relationships conform to
domain knowledge expectations.
Common Interpretability Techniques
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29
Figure 3. A model visualization in which partial dependence is dis‐
played with ICE for the input variable num9 (left). In this simulated
example, strong interactions exist between the input variables num1
and num4 and between num8 and num9. Notice how ICE curves
diverge from partial dependence for ~-1 < num9 < 1. Compare this to
Figure 1-2 to see how decision tree surrogates, ICE, and partial
dependence can be used together to find and confirm modeled interac‐
tions. Also note that in the histogram for num9 (right) data values for
num9 less than -3 and greater than 3 are very rare. Predictions for
such values could be untrustworthy due to the lack of available train‐
ing data. (Figure courtesy of Patrick Hall and H2O.ai.)
Table 13. A description of the residual plot model visualization technique
Technique: Residual plots
Description: Residuals refer to the difference between the actual value of a target variable and the
predicted value of a target variable for every row in a dataset. Residuals can be plotted in 2D to
analyze complex predictive models.
Suggested usage: Debugging for any machine learning model. Plotting the residual values
against the predicted values is a time-honored model assessment technique and a great way to find
outliers and see all of your modeling results in two dimensions.
OSS:
DALEX
themis-ml
Interpretable Machine Learning with Python
Global or local scope: Global when used
to assess the goodness-of-fit for a model
over an entire dataset. Local when used to
diagnose how a model treats a single row
or small group of rows.
Best-suited complexity: Any. Can be used to assess
machine learning models of varying complexity,
including linear, nonlinear, and nonmonotonic
functions.
Model specific or model agnostic:
Model agnostic.
Trust and understanding: Residual analysis can
promote understanding by guiding users toward
problematic predictions and enabling users to debug
such problems. It can enhance trust when residuals
are appropriately distributed and other fit statistics
(i.e., R2, AUC, etc.) are in the appropriate ranges.
30
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An Introduction to Machine Learning Interpretability
Variable importance
Variable importance is one of the most central aspects of explaining
machine learning models. There are many methods for calculating
variable importance and the methods tell us how much an input
variable contributed to the predictions of a model, either globally or
locally. While a handful of more established global variable impor‐
tance metrics do not arise from the aggregation of local measures,
averaging (or otherwise aggregating) local measures into global
measures has become popular recently. So, we’ll start by discussing
newer methods for local variable importance below and then move
onto global methods.
Deriving local variable importance for reason codes. Determining which
input variables impacted a specific prediction is crucial to explana‐
tion. Local variable importance, reason codes, turn-down codes, and
adverse action notices are several of the ways we make this determi‐
nation. Local variable importance refers to the raw values that show
how much a variable contributed to a prediction and the latter
phrases mostly come from credit scoring. Reason codes are plaintext explanations of a model prediction in terms of a model’s input
variables. Turn-down codes and adverse action notices refer to
another step of postprocessing where local variable importance and
reason codes are matched to legal reasons a loan or employment
application can be denied. We’ll stick with the more general phrases,
local variable importance and reason codes, in this section. These
should provide the raw data and information needed to meet the
higher bar of adverse action notices in many cases.
Aside from enabling appeal, reason codes are so important for
machine learning interpretability in applied settings because they
tell practitioners why a model makes a decision in terms of the mod‐
el’s input variables, and they can help practitioners understand if
high weight is being given to potentially problematic inputs includ‐
ing gender, age, marital status, or disability status. Of course, gener‐
ating reason codes for linear models is nothing new to banks, credit
bureaus, and other entities. The techniques described in Tables 1-14
through 1-18 are interesting as you can apply them to generate rea‐
son codes for potentially more accurate machine learning models.
Depending on your application you may have different needs and
expectations from your local variable importance and reason code
techniques. The best technique today appears to be Shapley local
Common Interpretability Techniques
|
31
variable importance. Though an exact method with strong theoreti‐
cal guarantees, it’s a little time-consuming to calculate, even for treebased models. (For other types of models, it can be infeasible.) Some
other techniques are approximate, but work on nearly any model,
such as LIME and leave-one-covariate-out (LOCO) variable impor‐
tance. LIME also has the nice ability to generate “sparse” explana‐
tions, or explanations that only use the most important variables.
The anchors technique has that same benefit, can be a bit more
accurate, and generates rules, instead of numeric values, about the
most important variables for a prediction. Variants of LIME, LOCO,
and treeinterpreter have the advantage of being able to generate
explanations extremely quickly for real-time explanations, but will
likely not be as accurate as Shapley explanations.
We’ll give you three pieces of advice before moving onto the techni‐
ques themselves:
1. Use Shapley if you can (and maybe even consider designing
your project around using Shapley with tree-based models).
2. Don’t hesitate to mix reason code techniques with interpretable
models to get the best of both worlds like we did in Figure 1-4.
3. If your machine learning system will affect humans, please
remember it will make wrong decisions, and explanations are
needed by the human subjects of those wrong decisions to
appeal your system’s erroneous predictions.
Pairing a globally interpretable model—a single decision tree—with
a local variable importance method—Shapley values—shows in
Figure 1-4 the entire directed graph of the model’s decision policies
as well as the exact numeric contribution of each input variable to
any prediction.
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An Introduction to Machine Learning Interpretability
Figure 4. Here, the decision policy of a high risk of default individual is
highlighted and the local Shapley variable importance values are pre‐
sented for that same individual. (Figure courtesy of Patrick Hall and
H2O.ai.)
Table 14. A description of the anchors local variable importance or reason
code technique
Technique: Anchors
Description: A newer approach from the inventors of LIME that generates high-precision sets of
plain-language rules to describe a machine learning model prediction in terms of the model’s input
variable values.
Suggested usage: Anchors is currently most applicable to classification problems in both
traditional data mining and pattern-recognition domains. Anchors can be higher precision than
LIME and generates rules about the most important variables for a prediction, so it can be a
potential replacement for Shapley values for models that don’t yet support the efficient calculation
of Shapley values.
Reference:
Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin, “Anchors: High-Precision Model-Agnostic
Explanations,” The Thirty-Second AAAI Conference on Artificial Intelligence (AAAI-18), April 25,
2018, https://oreil.ly/2OWwzSb.
OSS: anchor
Global or local scope: Local.
Best-suited complexity: Low to medium. Anchors can create explanations for very complex
functions, but the rule set needed to describe the prediction can become large.
Model specific or model agnostic: Model agnostic.
Common Interpretability Techniques
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33
Trust and understanding: Anchor explanations increase understanding by creating explanations
for each prediction in a dataset. They enhance trust when the important variables for specific
records conform to human domain knowledge and reasonable expectations.
Table 15. A description of the LOCO local variable importance or reason
code technique
Technique: LOCO variable importance
Description: LOCO, or even LOFO, variously stands for leave-one-{"column” or “covariate” or
“feature"}-out. LOCO creates local interpretations for each row in a training or unlabeled score set
by scoring the row of data once and then again for each input variable (e.g., column, covariate,
feature) in the row. In each additional scoring run, one input variable is set to missing, zero, its
mean value, or another appropriate value for leaving it out of the prediction. The input variable
with the largest absolute impact on the prediction for that row is taken to be the most important
variable for that row’s prediction. Variables can also be ranked by their impact on the prediction on
a per-row basis.
Suggested usage: You can use LOCO to build reason codes for each row of data on which nearly
any complex model makes a prediction. LOCO can deteriorate in accuracy when complex nonlinear
dependencies exist in a model. Shapley explanations might be a better technique in this case, but
LOCO is model agnostic and has speed advantages over Shapley both in training and scoring new
data.
Reference:
Jing Lei et al., “Distribution-Free Predictive Inference for Regression,” arXiv:1604.04173, 2016,
https://arxiv.org/pdf/1604.04173v1.pdf.
OSS:
conformal
Interpretable Machine Learning with Python
Global or local scope: Local but can be
aggregated to create global explanations.
Best-suited complexity: Any. LOCO measures
are most useful for nonlinear, nonmonotonic
response functions but can be applied to many
types of machine-learned response functions.
Model specific or model agnostic: Model agnostic.
Trust and understanding: LOCO measures increase understanding because they tell us the most
influential variables in a model for a particular observation and their relative rank. LOCO measures
increase trust if they are in line with human domain knowledge and reasonable expectations.
Table 16. A description of the LIME local variable importance or reason
code technique
Technique: LIME
Description: Typically uses local linear surrogate models to explain regions in a complex machinelearned response function around an observation of interest.
34
| An Introduction to Machine Learning Interpretability
Suggested usage: Local linear model parameters can be used to describe the average behavior of
a complex machine-learned response function around an observation of interest and to construct
reason codes. LIME is approximate, but has the distinct advantage of being able to generate sparse,
or simplified, explanations using only the most important local variables. Appropriate for pattern
recognition applications as well. The original LIME implementation may sometimes be
inappropriate for generating explanations in real-time on unseen data.
Reference:
Ribeiro et al., “‘Why Should I Trust You?' Explaining the Predictions of Any Classifier.”
OSS:
eli5
iml
lime (Python)
lime (R)
Skater
Interpretable Machine Learning with Python
Best-suited complexity: Low to medium. Suited for response functions of high complexity but
can fail in regions of extreme nonlinearity or high-degree interactions.
Global or local scope: Local.
Model specific or model agnostic: Model agnostic.
Trust and understanding: LIME increases transparency by revealing important input variables
and their linear trends. LIME bolsters trust when the important variables and their linear trends
around specific records conform to human domain knowledge and reasonable expectations.
Table 17. A description of the treeinterpreter local variable importance or
reason code technique
Technique: Treeinterpreter
Description: For each variable used in a model, treeinterpreter decomposes some decision tree,
random forest, and GBM predictions into bias (overall training data average) and component terms.
Treeinterpreter simply outputs a list of the bias and individual variable contributions globally and
for each record.
Suggested usage: You can use treeinterpreter to interpret some complex tree-based models, and
to create reason codes for each prediction. If you would like to use treeinterpreter, make sure your
modeling library is fully supported by treeinterpreter. In some cases, treeinterpreter may not be
locally accurate (local contributions do not sum to the model prediction) and treeinterpreter does
not consider how contributions of many variables affect one another as carefully as the Shapley
approach. However, treeinterpreter can generate explanations quickly. Also most treeinterpreter
techniques appear as Python packages.
Reference:
Ando Saabas, “Random Forest Interpretation with scikit-learn,” Diving into Data [blog], August 12,
2015, https://oreil.ly/33CtCK2.
OSS:
eli5
treeinterpreter
Common Interpretability Techniques
|
35
Global or local scope: Local but can be
aggregated to create global explanations.
Best-suited complexity: Any. Treeinterpreter is
meant to explain the usually nonlinear,
nonmonotonic response functions created by
certain decision tree, random forest, and GBM
algorithms.
Model specific or model agnostic: Treeinterpreter is model specific to algorithms based on
decision trees.
Trust and understanding: Treeinterpreter increases understanding by displaying ranked
contributions of input variables to the predictions of decision tree models. Treeinterpreter enhances
trust when displayed variable contributions conform to human domain knowledge or reasonable
expectations.
Table 18. A description of the Shapley local variable importance or reason
code technique
Technique: Shapley explanations
Description: Shapley explanations are a Nobel-laureate technique with credible theoretical support
from economics and game theory. Shapley explanations unify approaches such as LIME, LOCO, and
treeinterpreter to derive consistent local variable contributions to black-box model predictions.
Shapley also creates consistent, accurate global variable importance measures.
Suggested usage: Shapley explanations are accurate, local contributions of input variables and
can be rank-ordered to generate reason codes. Shapley explanations have long-standing theoretical
support, which might make them more suitable for use in regulated industries, but they can be
time consuming to calculate, especially outside of decision trees in H2O.ai, LightGBM, and XGBoost
where Shapley is supported in low-level code and uses the efficient Tree SHAP approach.
Reference:
Lundberg and Lee, “A Unified Approach to Interpreting Model Predictions.”
OSS:
h2o.ai
iml
LightGBM
shap
ShapleyR
shapper
XGBoost
Interpretable Machine Learning with Python
Global or local scope: Local but can be
aggregated to create global explanations.
36
|
Best-suited complexity: Low to medium. This
method applies to any machine learning model,
including nonlinear and nonmonotonic models, but
can be extremely slow for large numbers of
variables or deep trees.
An Introduction to Machine Learning Interpretability
Model specific or model agnostic: Can be
both. Uses a variant of LIME for modelagnostic explanations. Takes advantage of
tree structures for decision tree models and
is recommended for tree-based models.
Trust and understanding: Shapley explanations
enhance understanding by creating accurate
explanations for each observation in a dataset. They
bolster trust when the important variables for
specific records conform to human domain
knowledge and reasonable expectations.
Global variable importance measures. Unlike local variable importance
or reason code methods, global variable importance methods quan‐
tify the global contribution of each input variable to the predictions
of a complex machine learning model over an entire dataset, not just
for one individual or row of data. Global variable importance met‐
rics can be calculated many ways, by the LOCO method, by shuf‐
fling variable values and investigating the difference in model
scores, by the Shapley method, or by many other model-specific
methods. Variable importance measures are typically seen in treebased models but are also reported for other models. A simple heu‐
ristic rule for variable importance in a decision tree is related to the
depth and frequency at which a variable is split in a tree, where vari‐
ables used higher in the tree and more frequently in the tree are
more important. For artificial neural networks, variable importance
measures are typically associated with the aggregated, absolute mag‐
nitude of model parameters for a given variable of interest.
For some nonlinear, nonmonotonic response functions, global vari‐
able importance measures are the only commonly available, effi‐
cient, quantitative measure of the machine-learned relationships
between input variables and the prediction target in a model. Vari‐
able importance measures sometimes give insight into the average
direction that a variable pushes the response function, and some‐
times they don’t. At their most basic, they simply state the magni‐
tude of a variable’s relationship with the response as compared to
other variables used in the model. This is hardly ever a bad thing to
know, and since most global variable importance measures are older
approaches, they are often expected by model validation teams. Like
local variable importance, if you have the patience or ability to cal‐
culate Shapley values, they are likely the most accurate variable
importance metric. Most others are approximate or inconsistent,
but they are certainly still useful. In fact, comparing the differences
between the imperfect results of several global variable importance
techniques can help you reason about the overall drivers of your
model’s behavior (see Table 1-19).
Common Interpretability Techniques
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37
Table 19. A description of global variable importance techniques
Technique: Global variable importance
Suggested usage: Understanding an input variable’s global contribution to model predictions.
Practitioners should be aware that unsophisticated measures of variable importance can be biased
toward larger-scale variables or variables with a high number of categories. Global variable
importance measures are typically not appropriate for creating reason codes.
References:
Hastie et al., The Elements of Statistical Learning.
Jerome Friedman, “Greedy Function Approximation: A Gradient Boosting Machine,” IMS 1999 Reitz
Lecture, April 19, 2001, https://oreil.ly/2yZr3Du.
Leo Breiman, “Random Forests,” Machine Learning 45, no. 1 (2001): 5–32. https://oreil.ly/30c4Jml.
Lundberg and Lee, “A Unified Approach to Interpreting Model Predictions.”
OSS:
DALEX
h2o.ai
iml
lofo-importance
LightGBM
shap
ShapleyR
shapper
Skater
vip
XGBoost
R (various packages)
scikit-learn (various functions)
Interpretable Machine Learning with Python
Global or local scope: Global.
Best-suited complexity: Any. Variable importance measures are most useful for nonlinear, nonmonotonic response functions but can be applied to many types of machine-learned response
functions.
Model specific or model agnostic: Both. Some global variable importance techniques are
typically model specific, but the LOCO, permutation, and Shapley approaches are model agnostic.
Trust and understanding: Variable importance measures increase understanding because they
tell us the most influential variables in a model and their relative rank. Variable importance
measures increase trust if they are in line with human domain knowledge and reasonable
expectations.
Fairness
As we discussed earlier, fairness is yet another important facet of
interpretability, and a necessity for any machine learning project
whose outcome will affect humans. Traditional checks for fairness,
often called disparate impact analysis, typically include assessing
model predictions and errors across sensitive demographic seg‐
38
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An Introduction to Machine Learning Interpretability
ments of ethnicity or gender. Today the study of fairness in machine
learning is widening and progressing rapidly, including the develop‐
ment of techniques to remove bias from training data and from
model predictions, and also models that learn to make fair predic‐
tions. A few of the many new techniques are presented in Tables
1-20 to 1-23. To stay up to date on new developments for fairness
techniques, keep an eye on the public and free Fairness and Machine
Learning book and https://fairmlbook.org.
Table 20. A description of the disparate impact testing fairness techniques
Technique: Disparate impact testing
Description: A set of simple tests that show differences in model predictions and errors across
demographic segments.
Suggested usage: Use for any machine learning system that will affect humans to test for biases
involving gender, ethnicity, marital status, disability status, or any other segment of possible
concern. If disparate impact is discovered, use a remediation strategy (Tables 1-21 to 1-23), or
select an alternative model with less disparate impact. Model selection by minimal disparate impact
is probably the most conservative remediation approach, and may be most appropriate for
practitioners in regulated industries.
Reference:
Feldman et al., “Certifying and Removing Disparate Impact.”
OSS:
aequitas
AIF360
Themis
themis-ml
Interpretable Machine Learning with Python
Global or local scope: Global because
fairness is measured across demographic
groups, not for individuals.
Best-suited complexity: Low to medium. May fail
to detect local instances of discrimination in very
complex models.
Model specific or model agnostic:
Model agnostic.
Trust and understanding: Mostly trust as
disparate impact testing can certify the fairness of a
model, but typically does not reveal the causes of
any discovered bias.
Table 21. A description of the reweighing fairness preprocessing technique
Technique: Reweighing
Description: Preprocesses data by reweighing the individuals in each demographic group
differently to ensure fairness before model training.
Suggested usage: Use when bias is discovered during disparate impact testing; best suited for
classification.
Common Interpretability Techniques
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39
Reference: Faisal Kamiran and Toon Calders, “Data Preprocessing Techniques for Classification
Without Discrimination,” Knowledge and Information Systems 33, no. 1 (2012): 1–33. https://
oreil.ly/2Z3me6W.
OSS: AIF360
Global or local scope: Global because
fairness is measured across demographic
groups, not for individuals.
Best-suited complexity: Low to medium. May fail
to remediate local instances of discrimination in
very complex models.
Model specific or model agnostic: Model
agnostic, but mostly meant for classification
models.
Trust and understanding: Mostly trust, because
the process simply decreases disparate impact in
model results by reweighing the training dataset.
Table 22. A description of the adversarial debiasing fair modeling
technique
Technique: Adversarial debiasing
Description: Trains a model with minimal disparate impact using a main model and an adversarial
model. The main model learns to predict the outcome of interest, while minimizing the ability of
the adversarial model to predict demographic groups based on the main model predictions.
Suggested usage: When disparate impact is detected, use adversarial debiasing to directly train a
model with minimal disparate impact without modifying your training data or predictions.
Reference: Brian Hu Zhang, Blake Lemoine, and Margaret Mitchell, “Mitigating Unwanted Biases
with Adversarial Learning,” arXiv:1801.07593, 2018, https://oreil.ly/2H4rvVm.
OSS: AIF360
Global or local scope: Potentially both
because the adversary may be complex
enough to discover individual instances of
discrimination.
Best-suited complexity: Any. Can train
nonlinear, nonmonotonic models with minimal
disparate impact.
Model specific or model agnostic: Model
agnostic.
Trust and understanding: Mostly trust,
because the process simply decreases disparate
impact in a model.
Table 23. A description of the reject option-based classification
postprocessing fairness technique
Technique: Reject option-based classification
Description: Postprocesses modeling results to decrease disparate impact; switches positive and
negative labels in unprivileged groups for individuals who are close to the decision boundary of a
classifier to decrease discrimination.
Suggested usage: Use when bias is discovered during disparate impact testing; best suited for
classification.
Reference: Faisal Kamiran, Asim Karim, and Xiangliang Zhang, “Decision Theory for DiscriminationAware Classification,” IEEE 12th International Conference on Data Mining (2012): 924-929. https://
oreil.ly/2Z7MNId.
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An Introduction to Machine Learning Interpretability
OSS:
AIF360
themis-ml
Global or local scope: Global because fairness Best-suited complexity: Low. Best suited for
is measured across demographic groups, not
linear classifiers.
for individuals.
Model specific or model agnostic: Model
agnostic, but best suited for linear classifiers
(i.e., logistic regression and naive Bayes).
Trust and understanding: Mostly trust,
because the process simply decreases disparate
impact in model results by changing some
results.
Sensitivity Analysis and Model Debugging
Sensitivity analysis investigates whether model behavior and outputs
remain acceptable when data is intentionally perturbed or other
changes are simulated in data. Beyond traditional assessment practi‐
ces, sensitivity analysis of predictions is perhaps the most important
validation and debugging technique for machine learning models.
In practice, many linear model validation techniques focus on the
numerical instability of regression parameters due to correlation
between input variables or between input variables and the target
variable. It can be prudent for those switching from linear modeling
techniques to machine learning techniques to focus less on numeri‐
cal instability of model parameters and to focus more on the poten‐
tial instability of model predictions.
One of the main thrusts of linear model validation is sniffing out
correlation in the training data that could lead to model parameter
instability and low-quality predictions on new data. The regulariza‐
tion built into most machine learning algorithms makes their
parameters and rules more accurate in the presence of correlated
inputs, but as discussed repeatedly, machine learning algorithms can
produce very complex nonlinear, nonmonotonic response functions
that can produce wildly varying predictions for only minor changes
in input variable values. Because of this, in the context of machine
learning, directly testing a model’s predictions on simulated, unseen
data, such as recession conditions, is likely a better use of time than
searching through static training data for hidden correlations.
Single rows of data with the ability to swing model predictions are
often called adversarial examples. Adversarial examples are
extremely valuable from a security and model debugging perspec‐
tive. If we can easily find adversarial examples that cause model pre‐
Common Interpretability Techniques
|
41
dictions to flip from positive to negative outcomes (or vice versa)
this means a malicious actor can game your model. This security
vulnerability needs to be fixed by training a more stable model or by
monitoring for adversarial examples in real time. Adversarial exam‐
ples are also helpful for finding basic accuracy and software prob‐
lems in your machine learning model. For instance, test your
model’s predictions on negative incomes or ages, use character val‐
ues instead of numeric values for certain variables, or try input vari‐
able values 10% to 20% larger in magnitude than would ever be
expected to be encountered in new data. If you can’t think of any
interesting situations or corner cases, simply try a random data
attack: score many random adversaries with your machine learning
model and analyze the resulting predictions (Table 1-24). You will
likely be surprised by what you find.
Table 24. A description of sensitivity analysis and adversarial examples
Technique: Sensitivity analysis and adversarial examples
Suggested usage: Testing machine learning model predictions for accuracy, fairness, security, and
stability using simulated datasets, or single rows of data, known as adversarial examples. If you are
using a machine learning model, you should probably be conducting sensitivity analysis.
OSS:
cleverhans
foolbox
What-If Tool
Interpretable Machine Learning with Python
Global or local scope: Sensitivity analysis can be a global interpretation technique when many
input rows to a model are perturbed, scored, and checked for problems, or when global
interpretation techniques are used with the analysis, such as using a single, global surrogate model
to ensure major interactions remain stable when data is lightly and purposely corrupted. Sensitivity
analysis can be a local technique when an adversarial example is generated, scored, and checked or
when local interpretation techniques are used with adversarial examples (e.g., using LIME to
determine if the important variables in a credit allocation decision remain stable for a given
customer after perturbing their data values). In fact, nearly any technique in this section can be
used in the context of sensitivity analysis to determine whether visualizations, models,
explanations, or fairness metrics remain stable globally or locally when data is perturbed in
interesting ways.
Best-suited complexity: Any. Sensitivity analysis can help explain the predictions of nearly any
type of response function, but it is probably most appropriate for nonlinear response functions and
response functions that model high-degree variable interactions. For both cases, small changes in
input variable values can result in large changes in a predicted response.
Model specific or model agnostic: Model agnostic.
42
| An Introduction to Machine Learning Interpretability
Trust and understanding: Sensitivity analysis enhances understanding because it shows a
model’s likely behavior and output in important situations, and how a model’s behavior and output
may change over time. Sensitivity analysis enhances trust when a model’s behavior and outputs
remain stable when data is subtly and intentionally corrupted. It also increases trust if models
adhere to human domain knowledge and expectations when interesting situations are simulated,
or as data changes over time.
Updating Your Workflow
Now that you’ve read about these machine learning interpretability
techniques, you may be wondering how to fit them into your profes‐
sional workflow. Figure 1-5 shows one way to augment the standard
data mining workflow with steps for increasing accuracy, interpreta‐
bility, privacy, security, transparency, and trustworthiness using the
classes of techniques introduced in this section.
Figure 5. A proposed holistic training and deployment workflow for
human-centered or other high-stakes machine learning applications.
(Figure courtesy of Patrick Hall and H2O.ai. For more details on this
workflow, please see: https://github.com/jphall663/hc_ml.)
We suggest using the introduced techniques in these workflow steps.
For instance, you may visualize and explore your data using projec‐
tions and network graphs, preprocess your data using fairness
reweighing, and train a monotonic GBM model. You might then
explain the monotonic GBM with a combination of techniques such
Common Interpretability Techniques
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43
as decision tree surrogates, partial dependence and ICE plots, and
Shapley explanations. Then you could conduct disparate impact
testing to ensure fairness in your predictions and debug your model
with sensitivity analysis. Such a combination represents a current
best guess for a viable human-centered, or other high-stakes appli‐
cation, machine learning workflow.
Limitations and Precautions
By this point we hope that you can see the tremendous intellectual,
social, and commercial potential for interpretable machine learning
models and debugging, explanation, and fairness techniques. And
though we’ve tried to present a balanced, practical portrait of the
technologies, it’s important to call out some specific limitations and
precautions. Like many technologies, machine learning explanations
can be abused, particularly when used as a faulty safeguard for
harmful black boxes (e.g., fairwashing) to make a biased model
appear fair.38 Explanations can also be used for malicious hacking, to
steal predictive models, to steal sensitive training data, and to plan
other more sophisticated attacks.39,40 In addition to fairwashing and
hacking, there are at least three other general concerns to be aware
of: the idea that explanations alone do not equal trust, the multiplic‐
ity of good models, and the limitations of surrogate models.
Explanations Alone Foster Understanding and
Appeal, Not Trust
While they are likely necessary for trust in many cases, explanations
are certainly not sufficient for trust in all cases.41 Explanation, as a
general concept, is related more directly to understanding and
transparency than to trust (as shown by the Merriam-Webster defi‐
38 Ulrich Aïvodji et al., “Fairwashing: The Risk of Rationalization,” arXiv:1901.09749,
2019, https://arxiv.org/pdf/1901.09749.pdf.
39 Reza Shokri et al., “Membership Inference Attacks Against Machine Learning Models,”
IEEE Symposium on Security and Privacy (SP), 2017, https://oreil.ly/2Z22LHI.
40 Florian Tramèr et al., “Stealing Machine Learning Models via Prediction APIs,” in 25th
{USENIX} Security Symposium ({USENIX} Security 16) (2016): 601–618. https://
oreil.ly/2z1TDnC.
41 Patrick Hall, “Guidelines for the Responsible and Human-Centered Use of Explainable
Machine Learning,” arXiv:1906.03533, 2019, https://arxiv.org/pdf/1906.03533.pdf.
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nition, which doesn’t mention trust) Simply put, you can understand
and explain a model without trusting it. You can also trust a model
and not be able to understand or explain it. Consider the following
example scenarios:
• Explanation and understanding without trust: In Figure 1-6,
global Shapley explanations and residual analysis identify a
pathology in an unconstrained GBM model trained to predict
credit card default. The GBM overemphasizes the input variable
PAY_0, or a customer’s most recent repayment status. Due to
overemphasis of PAY_0, the GBM usually can’t predict on-time
payment if recent payments are delayed (PAY_0 > 1), causing
large negative residuals. The GBM also usually can’t predict
default if recent payments are made on time (PAY_0 ≤ 1), caus‐
ing large positive residuals. In this example scenario, a machine
learning model is explainable, but not trustworthy.
• Trust without explanation and understanding: Years before
reliable explanation techniques were widely acknowledged and
available, black-box predictive models, such as autoencoder and
MLP neural networks, were used for fraud detection in the
financial services industry.42 When these models performed
well, they were trusted.43 However, they were not explainable or
well understood by contemporary standards.
If trust in models is your goal, then explanations alone are not suffi‐
cient. However, in an ideal scenario, we would all use explanation
techniques with a wide variety of other methods to increase accu‐
racy, fairness, interpretability, privacy, security, and trust in machine
learning models.
42 Krishna M. Gopinathan et al., “Fraud Detection Using Predictive Modeling,” October 6,
1998. US Patent 5,819,226. https://oreil.ly/2Z3FLIn.
43 “Reduce Losses from Fraudulent Transactions,” SAS [company site]. https://oreil.ly/
2KwolMk.
Limitations and Precautions
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45
Figure 6. Explanatory and model debugging techniques show us why a
machine learning model isn’t trustworthy: this machine learning model
is too dependent on one input variable, PAY_0. The model makes
many errors because of its overemphasis of that variable. (Figure cour‐
tesy of Patrick Hall and H2O.ai.)
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The Multiplicity of Good Models
For the same set of input variables and prediction targets, complex
machine learning algorithms can produce multiple accurate models
with very similar, but not the same, internal architectures. It is
important to remember that details of explanations and fairness can
change across multiple accurate, similar models trained on the same
data! This difficult mathematical problem goes by several names. In
his seminal 2001 paper, Professor Leo Breiman of UC Berkeley
called this problem the multiplicity of good models.44 Some in credit
scoring refer to this same phenomenon as model locality. Whatever
you call it, this means almost every debugging, explanation, or fair‐
ness exercise on a complex machine learning model assumes we are
choosing to debug, explain, or audit for fairness just one of many,
many similar models. Let’s discuss why this happens and what can
be done to address it.
Figures 1-7 and 1-8 are cartoon illustrations of the surfaces defined
by error functions for two fictitious predictive models. In Figure 1-7
the error function is representative of a traditional linear model’s
error function. The surface created by the error function in
Figure 1-7 is convex. It has a clear global minimum in three dimen‐
sions, meaning that given two input variables, such as a customer’s
income and a customer’s interest rate, the most accurate model
trained to predict loan defaults (or any other outcome) would
almost always give the same weight to each input in the prediction,
and the location of the minimum of the error function and the
weights for the inputs would be unlikely to change very much if the
model was retrained, even if the input data about a customer’s
income and interest rate changed a little bit. (The actual numeric
values for the weights could be ascertained by tracing a straight line
from the minimum of the error function pictured in Figure 1-7 to
the interest rate axis [the X axis] and income axis [the Y axis].)
44 Leo Breiman, “Statistical Modeling: The Two Cultures (with Comments and a Rejoin‐
der by the Author),” Statistical Science 16, no. 3 (2001): 199-231. https://oreil.ly/303vbOJ.
Limitations and Precautions
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47
Figure 7. An illustration of the error surface of a traditional linear
model. (Figure courtesy of H2O.ai.)
Because of the convex nature of the error surface for linear models,
there is basically only one best model, given some relatively stable
set of inputs and a prediction target. The model associated with the
error surface displayed in Figure 1-7 would be said to have strong
model locality. Even if we retrained the model on new or updated
data, the weight of income versus interest rate is likely mostly stable
in the pictured error function and its associated linear model.
Explanations about how the function made decisions about loan
defaults based on those two inputs would also probably be stable
and so would results for disparate impact testing.
Figure 1-8 depicts a nonconvex error surface that is representative of
the error function for a machine learning function with two inputs
—for example, a customer’s income and a customer’s interest rate—
and an output, such as the same customer’s probability of defaulting
on a loan. This nonconvex error surface with no obvious global
minimum implies there are many different ways a complex machine
learning algorithm could learn to weigh a customer’s income and a
customer’s interest rate to make an accurate decision about when
they might default. Each of these different weightings would create a
different function for making loan default decisions, and each of
these different functions would have different explanations and fair‐
ness characteristics! This would likely be especially obvious upon
updating training data and trying to refit a similar machine learning
model.
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An Introduction to Machine Learning Interpretability
Figure 8. An illustration of the error surface of a machine learning
model. (Figure courtesy of H2O.ai.)
While there is no remedy to the multiplicity of good models chal‐
lenge in machine learning, Shapley values do often account for per‐
turbations of numerous similar models and constrained
interpretable models are probably your best bet for creating an accu‐
rate, stable, and representative model that won’t change too much if
your training data is updated. Also, the multiplicity of good models
is not necessarily always a problem. You can use it to your advantage
in some situations: of the many machine learning models you can
train for a given dataset, it’s possible that you can find one with the
desired accuracy, explanation, and fairness characteristics.
Limitations of Surrogate Models
Surrogate models are important explanation and debugging tools.
They can provide global and local insights into both model predic‐
tions and model residuals or errors. However, surrogate models are
approximate. There are few theoretical guarantees that the surrogate
model truly represents the more complex original model from
which it has been extracted. Let’s go over the rationale for surrogate
models and then outline the nuances of working with surrogate
models responsibly. Linear models, and other types of more
straightforward models, like the function in Figure 1-9, create
approximate models with neat, exact explanations. Surrogate models
are meant to accomplish the converse (i.e., approximate explana‐
tions for more exact models). In the cartoon illustrations in Figures
Limitations and Precautions
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49
1-9 and 1-10, we can see the benefit of accurate and responsible use
of surrogate models. The explanation for the simple interpretable
model in Figure 1-9 is very direct, but still doesn’t really explain the
modeled age versus purchasing behavior because the linear model
just isn’t fitting the data properly.
Figure 9. A linear model, g(x), predicts the average number of purcha‐
ses given a customer’s age. The predictions can be inaccurate but the
associated explanations are straightforward and stable. (Figure cour‐
tesy of H2O.ai.)
Although the explanations for the more complex machine learning
function in Figure 1-10 are approximate, they are at least as useful, if
not more so, than the linear model explanations above because the
underlying machine learning response function has learned more
exact information about the relationship between age and purcha‐
ses. Of course, surrogate models don’t always work out like our car‐
toon illustrations. So, it’s best to always measure the accuracy of
your surrogate models and to always pair them with more direct
explanation or debugging techniques.
When measuring the accuracy of surrogate models, always look at
the R2, or average squared error (ASE), between your surrogate
model predictions and the complex response function you are try‐
ing to explain. Also use cross-validated error metrics for decision
tree surrogate models. Single decision trees are known to be unsta‐
ble. Make sure your surrogate decision trees have low and stable
error across multiple folds of the dataset in which you would like to
create explanations.
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| An Introduction to Machine Learning Interpretability
Figure 10. A machine learning model, g(x), predicts the number of
purchases, given a customer’s age, very accurately, nearly replicating
the true, unknown signal-generating function, f(x). (Figure courtesy of
H2O.ai.)
Additionally, there are many options to pair surrogate models with
more direct techniques. In Figures 1-2 and 1-3 we’ve already shown
how to pair decision tree surrogate models with direct plots of
model predictions (i.e., ICE and partial dependence curves) to find
and confirm interactions. You can pair Shapley values with LIME
coefficients to see accurate point estimates of local variable impor‐
tance and the local linear trends of the same variables. You can also
pair decision tree surrogate models of residuals with direct adversa‐
rial perturbations to uncover specific error pathologies in your
machine learning models, and you can probably think of several
other ways to combine surrogate models and direct explanation,
fairness, or debugging techniques. Just remember that if your surro‐
gate model is not an accurate representation of the model you are
trying to explain, or if surrogate model explanations don’t match up
with more direct explanation techniques, you probably should not
use surrogate models for the interpretability task at hand.
Testing Interpretability and Fairness
The novelty and limitations of interpretable machine learning might
call into question the trustworthiness of debugging, explanation, or
fairness techniques themselves. Don’t fret! You can test these techni‐
ques for accuracy too. Originally, researchers proposed testing
machine learning model explanations by their capacity to enable
humans to correctly determine the outcome of a model prediction
Testing Interpretability and Fairness
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51
based on input values.45 Given that human evaluation studies are
likely impractical for some commercial data science or machine
learning groups, and that we’re not yet aware of any formal testing
methods for debugging or fairness techniques today, several poten‐
tial approaches for testing debugging, explanations, and fairness
techniques themselves are proposed here:
Simulated data
You can use simulated data with known characteristics to test
debugging, explanation, and fairness techniques. For instance,
models trained on totally random data with no relationship
between a number of input variables and a prediction target
should not give strong weight to any input variable, nor gener‐
ate compelling local explanations or reason codes. Nor should
they exhibit obvious fairness problems. Once this baseline has
been established, you can use simulated data with a known sig‐
nal generating function to test that explanations accurately rep‐
resent that known function. You can simulate data with known
global correlations and local dependencies between demo‐
graphic variables, or other proxy variables, and a prediction tar‐
get and ensure your fairness techniques find these known group
and individual fairness issues. You can also switch labels for
classification decisions or inject noise into predicted values for
regression models and check that model debugging techniques
find the simulated errors. Of course, this kind of empirical test‐
ing doesn’t guarantee theoretical soundness, but it can certainly
help build the case for using debugging, explanation, and fair‐
ness techniques for your next machine learning endeavor.
Explanation and fairness metric stability with increased prediction
accuracy
Another workable strategy for building trust in explanation and
fairness techniques may be to build from an established, previ‐
ously existing model with known explanations and acceptable
fairness characteristics. Essentially, you can perform tests to see
how accurate a model can become or how much its form can
change before its predictions’ reason codes veer away from
known standards and its fairness metrics drift in undesirable
45 Doshi-Velez and Kim, “Towards a Rigorous Science of Interpretable Machine Learn‐
ing.”
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An Introduction to Machine Learning Interpretability
ways. If previously known, accurate explanations or reason
codes from a simpler linear model are available, you can use
them as a reference for the accuracy of explanations from a
related, but more complex and hopefully more accurate, model.
The same principle likely applies for fairness metrics. Add new
variables one by one or increase the complexity of the model
form in steps, and at each step make sure fairness metrics
remain close to the original, trusted model’s measurements.
Debugging explanation and fairness techniques with sensitivity analy‐
sis and adversarial examples
If you agree that explanations and fairness metrics likely should
not change unpredictably for minor or logical changes in input
data, then you can use sensitivity analysis and adversarial exam‐
ples to debug explanation and fairness techniques. You can set
and test tolerable thresholds for allowable explanation or fair‐
ness value changes and then begin manually or automatically
perturbing input data and monitoring for unacceptable swings
in explanation or fairness values. If you don’t observe any
unnerving changes in these values, your explanation and fair‐
ness techniques are likely somewhat stable. If you do observe
instability, try a different technique or dig in and follow the trail
the debugging techniques started you down.
Machine Learning Interpretability in Action
To see how some of the interpretability techniques discussed in this
report might look and feel in action, a public, open source reposi‐
tory has been provided.
This repository contains examples of white-box models, model visu‐
alizations, reason code generation, disparate impact testing, and sen‐
sitivity analysis applied to the well-known Taiwanese credit card
customer dataset using the popular XGBoost and H2O libraries in
Python.46
46 D. Dua and C. Graff, UCI Machine Learning Repository, University of California
Irvine, School of Information and Computer Science, 2019. https://oreil.ly/33vI2LK.
Machine Learning Interpretability in Action
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53
Looking Forward
FATML, XAI, and machine learning interpretability are new, rapidly
changing, and expanding fields. Automated machine learning
(autoML) is another important new trend in artificial intelligence.
Several open source and proprietary software packages now build
machine learning models automatically with minimal human inter‐
vention. These new autoML systems tend to be even more complex,
and therefore potentially black box in nature, than today’s somewhat
human-oriented data science workflows. For the benefits of machine
learning and autoML to take hold across a broad cross-section of
industries, our cutting-edge autoML systems will also need to be
understandable and trustworthy.
In general, the widespread acceptance of machine learning inter‐
pretability techniques will be one of the most important factors in
the increasing adoption of machine learning and artificial intelli‐
gence in commercial applications and in our day-to-day lives. Hope‐
fully, this report has convinced you that interpretable machine
learning is technologically feasible. Now, let’s put these approaches
into practice, leave the ethical and technical concerns of black-box
machine learning in the past, and move on to a future of FATML
and XAI.
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An Introduction to Machine Learning Interpretability
Acknowledgments
We are thankful to colleagues past and present whose comments,
thoughts, and tips undoubtedly shaped our own thinking on the
topic of interpretable machine learning.
In particular, from H2O.ai, we thank SriSatish Ambati for putting
the resources of an amazing company behind our efforts. We thank
Mark Chan, Doug Deloy, Mateusz Dymczyk, Martin Dvorak, Ladi‐
slav Ligart, and Zac Taschdjian for their tireless efforts to turn the
ideas in this book into enterprise software. And we thank Pramit
Choudhary, Michal and Megan Kurka, Kerry O’Shea, Josephine
Wang, and Leland Wilkinson for additional ideas, guidance, and
software that are reflected in this report.
We also thank our colleagues from the broader interpretability com‐
munity for their expertise and input: Andrew Burt, Immuta; Mark
Chan, JPMC; Przemyslaw Biecek, Warsaw University of Technology;
Christoph Molnar, Ludwig-Maximilians-Universität München; Wen
Phan, Domino Data Labs; Nick Schmidt, BLDS, LLC; and Sameer
Singh, University of California, Irvine.
About the Authors
Patrick Hall is senior director for data science products at H2O.ai,
where he focuses mainly on model interpretability. Patrick is also
currently an adjunct professor in the Department of Decision Scien‐
ces at George Washington University, where he teaches graduate
classes in data mining and machine learning. Prior to joining
H2O.ai, Patrick held global customer-facing roles and research and
development roles at SAS Institute.
Navdeep Gill is a senior data scientist and software engineer at
H2O.ai, where he focuses mainly on machine learning interpretabil‐
ity. He previously focused on GPU accelerated machine learning,
automated machine learning, and the core H2O-3 platform. Prior to
joining H2O.ai, Navdeep worked at Cisco focusing on data science
and software development. Before that he was a researcher and ana‐
lyst in several neuroscience labs at California State University, East
Bay; University of California, San Francisco; and Smith Kettlewell
Eye Research Institute. Navdeep graduated from California State
University, East Bay with a MS in computational statistics, a BS in
statistics, and a BA in Psychology (minor in mathematics).